Quantum Synchronization of Twin Limit-Cycle Oscillators
arXiv:2502.21122 · doi:10.1103/f97j-474c
Abstract
Quantum synchronization has been a subject of intensive research in the last decade. In this work, we propose a quantum Liénard system whose classical equivalent features two limit cycles to one of which the system will converge. In the quantum case, both limit cycles coexist in a single steady state. Each of these limit cycles localizes to a distinct phase if coupled to an external drive: one quantum state can thus be assigned two phases. Furthermore, coupling two such oscillators leads to the simultaneous appearance of synchronization and a synchronization blockade. To shed light on this apparent paradoxical result, we introduce finer measures of quantum synchronization.
7+7 pages, 3+5 figures; corrected typos, added references, improved Fig. 2, added Section 2 in Supplemental Material with Fig. S2
References in corpus (36)
- Dynamical multistability in high-finesse micromechanical optical cavities
- Quantum synchronization of quantum van der Pol oscillators with trapped ions
- Quantum many-body dynamics in optomechanical arrays
- Measures of quantum synchronization in continuous variable systems
- Entanglement tongue and quantum synchronization of disordered oscillators
- Synchronization, quantum correlations and entanglement in oscillator networks
- Quantum synchronization of two Van der Pol oscillators
- Quantum synchronization and entanglement generation
- Mutual information as an order parameter for quantum synchronization
- Quantum correlations and mutual synchronization
- Spin Correlations as a Probe of Quantum Synchronization in Trapped Ion Phonon-Lasers
- Synchronizing the Smallest Possible System
- Quantum Synchronization Blockade: Energy Quantization hinders Synchronization of Identical Oscillators
- Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
- Noise-Induced Transitions in Optomechanical Synchronization
- Observation of quantum phase synchronization in spin-1 atoms
- Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
- Quantum synchronization in dimer atomic lattices
- Quantum limit-cycles and the Rayleigh and van der Pol oscillators
- Quantum Synchronisation in Nanoscale Heat Engines
- Noise-induced quantum synchronization
- Synchronization along quantum trajectories
- Synchronization in two-level quantum systems
- Topological synchronization of quantum van der Pol oscillators
- Observing Quantum Synchronization of a Single Trapped-Ion Qubit
- A phonon laser in the quantum regime
- Observation of quantum phase-synchronization in a nuclear spin-system
- The effect of Landau-Zener dynamics on phonon lasing
- Role of Coherence and Degeneracies in Quantum Synchronisation
- Synchronization and coalescence in a dissipative two-qubit system
- Symmetries and Synchronization Blockade
- Exotic synchronization in continuous time crystals outside the symmetric subspace
- Quantum synchronization through the interference blockade
- Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
- Liénard Type Nonlinear Oscillators and Quantum Solvability
- Microscopic quantum generalization of classical Liénard oscillators